In modern world I do not agree to purposely catch and keep wild birds except those guys in bird protection organization.
Only keep birds that are bred in captivity.

It may still look cruel to keep even birds that are bred in captivity but will such birds survive if we release them to the wild?
Hardly.
Not only because they grow up in captivity but also usually pet birds are not native to where it is kept.
Their bright color due to selective breeding easily attracts predator and may cause them to be elbowed out by the local bird community.
Keeping them actually helps 'keeping' them.
Even we can say that if they fly away it is due to curiosity instead of the desire of freedom.

One of the advantages of keeping bird than fish is you can bring the bird along when you travel in your own car so you do not have to worry that nobody feeds your bird.

The budgerigar (Melopsittacus undulatus), nicknamed budgie, is a type of small parrot with tiny beak.
It is commonly called parakeet in US.
It originates from Australia.
It was first kept as pet by the British.
Adult male has blue and smooth cere (waxy covering) around its nostrils.
Now with selective breeding there are quite a number of color varieties (besides green, now bright yellow, pale yellow, blue and white).
Compared to big parrots, it is difficult for budgies to learn talking.
There are rare cases that they imitate human speech.
They may imitate the sound of other bird and make you think that there is other bird around.
Yellow budgie actually makes me think of Looney Tunes Tweety, Sylvester and Granny.
I have been then told that Tweety is actually a canary (Serinus canaria).
If we already have other pet, we should not get a budgerigar not mainly because the pets may fight with each other but mainly because lest your attention will be spread thin.
Anyway if a budgie flies into your house, that may mean she is destined to be with you so you should keep her.

Budgies are the best choice for people who want to start keeping pet bird because they are:
1) as hardy as poultry.
2) small.
3) beautiful (I think among the beautiful birds in the world, it is the easiest to keep as pet).
4) not endangered, not caught from the wild. Widely bred in captivity.
5) not dangerous.
Some birds e.g. doves can be dangerous as their dropping is pathogenic.
6) not expensive.

My female budgie posing in front of camera. She is a recessive pied.

Cage

Criteria to purchase a cage:
a) Wooden, wicker, bamboo and plastic cage must not be used because the budgie will chew it.
b) The distance between two bars must be small enough that the bird cannot stick his neck out.
This does not only prevent escape, but also prevent accident that his neck is stuck between the bars.
c) The cage must have at least two food cups and two perches.
d) There should be a withdrawable tray for bird's dropping at the bottom.
e) The cage door should be able to shut down itself.
Sometimes we can forget to close the door after opening it and the bird flies away due to curiosity and does not know to come back.
f) It should be big enough that the bird can fly a little from one end to another.

Hang the cage.
Birds do not like to be looked at over their head.

Never put the cage near electrical cable.
The budgie will chew it.

Put the cage outdoor (to avoid particles of bird's dropping spreading in the house) but away from direct sunlight and rainwater (rainwater messes up the droppings).

Cleaning the bird cage can be undesirable.
To minimize the undesirability:
a) Put one or two layers of old newspaper (cut it to the suitable size) at the bottom of the cage.
b) Clean the cage at least once a week (if you have only one bird) so that the cleaning is easier (not that dirty).
If your cage is half metal half plastic, it is good to also detach the bottom plastic basin from the metal cage to clean it (not only cleaning the droppings tray).
When detaching, squeeze the metal cage (metal is flexible) instead of picking on the plastic to avoid breaking the plastic (plus it is very easy to detach by just squeezing the metal cage).

The bird

At the shop do not choose the bird that
a) is inactive.
If the shop keeps the birds in an air-conditioned room, most likely they will be all inactive and you can hardly tell which one is unhealthy.
b) has puffed up feathers.
c) has tumors especially on the face.
Of course you can do that if you know how to cure the bird.

I personally like a bird that is noisy, hehe. Also I will choose a friendly bird if there is one.
You want a pet that is friendly towards you, do you not?

Food

A budgie likes small seeds with hull.
At least two types of hulled seeds should be fed so that the bird is healthy.
Budgies love millet (Echinocholoa) seeds mixed with very little canary seed.
Sometimes give some cuttlefish bone (for calcium), vegetable or fruit.

Have two food cups for alternate use.
Take out dirty cup, wash it for next use.
Fill food into clean tray that has been washed during the last feeding.
When you are out for holidays, put two trays in.
Take serious note that a budgerigar can only survive 48 hours without food after the last feeding.

It is unnatural to have food available all the time.
You can put in the food cup in the morning (switch on the light if it is still not bright enough as most birds are nyctalopic except owls and penguins) and then take it out after a while when the bird stops eating.
Then in the evening again put back the food cup and later take it out.
By doing this
a) there will be less bird's dropping on the food cup.
b) you can ensure that there is enough food.
The food tray may look full but it is actually all husk.
You know it from the overall appearance and the weight of the content.
You may shake the food cup horizontally and if there is substantial rustle sound then it means there are still some seeds.
Blow the husk away before serving.
Use a tube to blow if you do not want the husk flying all over your face.
The hand holding the cup should be dry or else the husk will stick all over your wet hand.
c) the birds will be expecting you every time you approach the cage,
thus they will become friendlier towards you more quickly. This is a
way to tame a budgerigar.
d) the cup lasts longer because some birds like to bite the cup.
Well, if you think that is tedious and you want another option, then just take out the food cup when you are out for work and put it back when you come back from work.

The water should be human drinking water (not distilled or reversed osmotic water though).
Use water bottle so that the water is not contaminated by the bird's dropping, not to mention frequent water change and container wash.\
A budgerigar is smart enough to drink water from the tip of the tube.
If you think she is not drinking from the bottle, try manually feed her with it for a few times to let her know it.
Or just put both water cup and water bottle initially.

The bottle should:
a) be transparent so that the water level can be seen.
b) be tinted with dark color so that the algae will not grow so easily inside.
c) have two ball bearings.
The second ball bearing will add weight to the first one to seal the the tip of the tube better.

This water bottle is not tinted.

Playing

Budgerigars by nature like to play.
If the bird is single, she will play with you more.
But it is a little cruel if it is just because of this reason that you do not give her a mate.
You are not home always to be with her anyway.

If she is unfamiliar with you, she will flutter when you approach the cage.
That is normal.
Talk to her with gentle voice if you want.
Or you can whistle to her.
She likes it if you talk to her.
This is another way to tame a budgerigar.

Some budgerigars will sing along in their own language when you play music.

Handle with care.
She is very fragile.
When you catch her and her claws are grabbing on something, do not pull her forcibly.
Gently make her release her claws.

One bad point about budgerigars is they bite.
You need to endure the pain if you want to catch them in your hand.
If you play with them everyday, one day they will be friendly towards you and stop biting.

If you want you can play with the bird by letting the bird fly in your house.
Close all the doors and windows.
Switch off the fan.

On hot days spray mist on her.
You can let her take a quick warm-water bath.

Compatibility with other birds

If you have a bird and you want to add another one, put the newcomer straight into the cage and see if your bird bites the newcomer.
If the biting happens, you must let your bird get used to the newcomer first by putting the bird in another cage next to the main cage.

I had a finch with my budgie but they did not get along quit well so I gave away the finch.
I also once had an injured young sparrow that I rescued from the cat.
Although my budgie did not get along with the sparrow too but at least they lived in peace.
I released the sparrow after I was sure that she had recovered.
My budgie has some acquaintances, hehe.

Extra

Some people may suggest to clip four or five aviation feathers off one wing.
That can let you recapture the bird easily in case of accidental release.
Anyway I do not do that because I think she will feel uncomfortable with her wing manually stretched out and I am afraid she will be more exposed to predators if I am not aware of her accidental release.

Lack of exercise causes the bird's beak to overgrow.
Get it trimmed or else the bird cannot feed.
Use a nail clipper.
Clip a little by a little.
When the length is almost there, you should sense the bird's reaction by applying mild force on the clipper.
If the bird makes noise, it means you should not proceed anymore.

If there is no male in the cage but the female lay eggs, the eggs will not hatch.